Effective Teaching of Mathematics by Mr.V. Sundaram

Vol: 25
No: 2
An MDA Publication
September 2014
Madras Dyslexia Association
15, Sambasivam Street, Behind Jeeva Park, T. Nagar, Chennai 600 017 Tel: 2815 6697, 2815 7908
E-mail: [email protected]
Website: www.mdachennai.com
Effective Teaching of Mathematics
IN THIS ISSUE ...
Effective Teaching of
Mathematics
- Page 1 to 4
by Mr.V. Sundaram
This is transcribed from his presentation at MDA’s Samyukth 2013 with
his kind permission. The speaker describes some of the guidelines that
he has internally developed which seem to work in real life. He clarifies
about how Mathematics can be learnt by the children in an effective
way.
Math versus Language
Awareness and Setting up of
Resource Rooms
- Page 5
Children’s Page
- Page 6
News at MDA / ANANYA
- Page 7
MDA News Snippets
- Page 8
How many of us believe that in Primary school that Math should be
easier than language? Very few! With his vast experience, he is
convinced that Math learning is inherently easy for children. Language
cannot be learnt without an external source but Mathematics springs
from our own internal experience. Children see patterns around them.
All children intuitively understand concepts like more & less though
they may lack the vocabulary to express it. Any child who is presented
with 2 packets of sweets when asked to choose a packet may pick up
the larger one as he knows it has more.
The Math which arises within us is made more complicated and has
become difficult is because of 2 reasons:
• The language through which Math is taught. (Word problems are
more a language issue rather than a Math issue)
• The way Math is taught in schools. (Little or no allowance is given to
the nature of Math and the nature of the Primary Child)
Math is often taught in a very artificial way. It is taught like any other
subject. We use text books, home work, black board like in the
teaching of other subjects. Each subject taught in school is a varying
mix of:
• Concepts which need to be understood.
• Skills which need to be practiced
• Facts which need to be remembered
Moving…..
Teaching of Math and English are different
The Administrative Office of
MDA is in the process of
moving to the 1st Floor of
“Park View” near Jeeva Park,
94, G.N.Chetty Road, T.Nagar.
No changes in the telephone
numbers.
• Languages are mostly facts (vocabulary) and skills and less of
concepts (grammar & phonetic rules)
• Math is mostly abstract concepts and skills and less of facts. Hence
there should be almost no need for memorising.
• Therefore Language and Math need to be taught differently.
The only facts in Math are the way the 9 numerals and some symbols
are written and in fact everything else can be derived from one’s
thinking. There is no need to memorize anything if it is learnt in the
proper way.
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MDA Newsletter
Nature of the Primary School child
• Developmentally he/she is still in the concrete
operations stage
• Abstract concepts need to be presented visually or
with activity materials
• Facts need to be remembered by repeated use in
the appropriate context
• Skills need to be practiced with understanding
The Primary Child, according to Jean Piaget, is in the
concrete operation stage. When we teach him about
photosynthesis, he can repeat the word like repeating
the word patriotism. Repeating the words has no
connection to understanding.
Concepts should be presented visually or with activity
materials.
Odd and Even Numbers: Suppose a question is put
whether the people in this room are an odd or even
number? Instead of dividing by 2 if a pairing game is
played, if 1 is left without a pair it is odd, if all have
pairs then it is even. Then they realise
Odd number + even number = odd number
Even number + odd number = odd number
Even number + even number = even number
Odd number + odd number = even number
We all know 54 is an even number. When 5 is an odd
number why don’t we look at 5 and why are we
looking at 4 and call it even? This is because 5 is not
5 but 50. Any multiple of 10, 20, 30 is automatically an
even number. Children will not understand these
kind of concepts by lectures, they need to look at
concrete materials. They need to have bundles of
sticks (10) and understand that each bundle is
divisible by 2 and can be shared equally between two
people. This is the idea of even number.This is a
visual understanding of relations as otherwise it
results only in mugging up with no understanding.
Place Value: It is normally taught that 23 is 2 tens & 3
units and this does not make any sense to a child
though he/she is able to repeat it. If place value is not
mastered properly children have difficulty in addition,
subtraction and afterwards multiplication and division.
The basic numbers are only 0-9. The answer is in our
hands as we have only 10 fingers. All other numbers
are combinations of the 9 numbers only. It is
advisable to teach upto number 9 only, in the
Kindergarten classes and 0 upto 99, for 2 years in
September 2014
Classes 1 & 2 because it takes 2 years for them to
understand and represent numbers and play with
materials.
Various visual interpretations of “multiplying” and
“dividing” can be given. While multiplying 3 by 4 we
can have an array or 3 baskets of 4 fruits or 4
baskets of 3 fruits. Dr. A.R.Rao’s book “Proof by sight”
will throw a lot of light on those concepts that are
obvious and don’t need explanations.
Angles and Triangles: First let the children
understand the meaning of concepts. What is the
definition of an angle? They are never clear about
what is an angle and what is a triangle. They don’t
realize it is about the amount of rotation. Concepts
like ray, line and segment should come after Primary
when they are ready to understand it. Unnecessary
knowledge can be done away with in the lower
classes.
Concepts are also understood by playing around with
materials. While some activities can be done in class,
others need a special class like Math Lab. Math
Museum is different from a Math lab, as in the former
you mainly look at the exhibits. In the lab you prove by
doing experiments and demonstrate in terms of
materials, how numbers are different. The total cost of
Math Lab materials will not exceed Rs.200 as bottle
tops, ice-cream sticks, cardboard strips, rubber bands
are adequate.
Focus on understanding rather than labels
It is good to see that a child understands a concept
before you introduce the terms for it. When you teach
fractions more time should be spent on understanding
the connection between the number on top and
number at the bottom. The new terms numerator and
denominator and their spellings should not be the
focus. When the child becomes comfortable then the
terminology can be taught, otherwise they come in the
way of understanding.
Words in Math are often never used outside the
classroom, for e.g: predecessor, scalene, numerator,
denominator, improper number, surds, vulgar
fractions etc. There are words in Maths which have
different meanings outside the classroom rather than
inside, for e.g. acute, principal, interest, left (Social
and Math). We don’t make an effort to make them
understand, same word with a different meaning in
other spheres and in Math. So Math language
becomes a difficulty and playing games is a good way
of teaching it.
Right Angle: It is good to understand the importance
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MDA Newsletter
of the right angle and why it was called that. Also why
is the right angle the basis of classification? If we take
a sheet of paper and fold it to make a right angle we
can see it . We can also see what is less than and
more than the right angle. This is better than using a
protractor and getting confused. Why was the right
angle called the right angle? Some children thought it
was drawn to the right and so called that. It is
because a right angle can be made anywhere on the
Earth and it is the same as any other right angle
made on this earth. Euclid says all right angles are
equal. A mason builds a wall which is perpendicular.
The right angle is the easiest standard, it is a
concept.
Where do 90 and 360 come from? In olden days, they
counted the number of days that the Earth takes to
go around the Sun as 360, and divided it by 4. It gives
4 right angles and each quarter is 90 degrees. The
teacher needs to know how to explain a concept in
the form of a story, so that the concept will not be
forgotten.
Reduce writing
• Understanding is achieved by listening, speaking
and arguing.
• In the initial stages of understanding, writing takes
away time available for understanding.
• Writing steps etc can be done after understanding
has been achieved.
• Same is applicable in Geometry where a lot of time
is wasted in drawing geometrical figures rather than
understanding about them.
In a 40 minute period not many problems can be
solved and written. When they have a difficulty in
writing, it becomes worse. In the time it takes to write 2
problems, 10 problems can be discussed.
Understanding is more important and writing is the
last step. In Geometry, don’t ask them to construct
angles as they waste a lot of time. Give them 3 sticks.
Make an obtuse angle or acute angled triangle which
is more meaningful than wasting a whole period in
construction.
Irrelevance of pass mark in Math
• Math concepts are built hierarchically like a house
of cards.
• In Primary School, while learning basic skills,
whatever is learnt should be learnt 100%
• If a child has not mastered 1 digit addition there is
no way he/she can learn 2 digit additions.
September 2014
• Hence reduce the curriculum to the essentials and
ensure that these are learnt thoroughly.
• 35% (pass mark) may really mean 100% in addition, 50% in subtraction and 0% in multiplication.
The basic concepts have to be learnt thoroughly by
all children and more so in the Primary. Like toilet
training which can be 100%, children need to have
100% basic knowledge in Math. Only when you can
do addition of 1 digit number can you go on to doing
addition for 2 digit numbers.
Word problems
There are two kinds of issues with word problems.
• Understanding the language in which the problem
has been presented
• Relating the real life situation to a “Math operation
concept”
Let us have a story for 5-3=2. I have 5 chocolates
and I ate 3. If we say 5 birds are there, 3 fly away, it’s
a different story. I have 5 chocolates, my brother has
3 less than me. How many does he have? Subtraction
has come out of different life experiences, though
mathematically it can be summarized into 5-3, take
away, compare, less than, adding to subtract.
These are different life experiences in order to give
concrete form in the classroom.
Let us not call it a problem, but call it a Math story. Let
the children make problems with things that are close
to them, rather than the population or voters etc.
Pitfalls of textbooks
• Math curriculum is best covered in a spiral manner,
revisiting the same concept periodically at ever
increasing levels of understanding.
• Textbooks force us to cover the curriculum in a
linear fashion.
• When we cover fractions in 2 months and then
decimals in the next 2 months during which fractions are never revisited, students tend to forget
whatever they learnt of fractions.
• Use textbooks with care.
Give smaller numbers for the children to understand
the concept and to work with ease. 4 Kgs makes more
sense rather than 4000 gms. Giving a mixture of
problems is more useful than giving problems with the
same concept. When a child was asked where would
you find a subtraction sum she answered at the end
of a subtraction chapter.
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MDA Newsletter
September 2014
Autonomy to students
• Motivation levels of students increase if they have
a degree of autonomy in the classroom.
• Let students make their own problems & explore
the results.
• Encourage group work, discussions and peer
interactions.
Proof of the Pudding
The speaker shares these experiences with
conviction as he has seen the results.
• Many of these methods were tried out in Math and
in English in his previous school.
• In 3 years, Math went from being the most hated
subject to the most loved subject and even first
generation students were able to express themselves in simple English by Class 2.
So Maths has to be done at a spiral way. It has to be
revisited and then should go higher and higher
building on the basics. Math is full of such surprises,
let’s bring it into the classroom. Ask them to choose
numbers from 1-9 and do a 3 into 2 digit
multiplication. Teachers may wonder if you give so
many different kinds, then how can you check. Give a
calculator and let them check. Let them involve their
parents, siblings and be happy doing it. Joy of
learning and working should be instilled, so that they
are motivated to work.
The speaker Mr.V.Sundaram is a B.Tech from IIT
Mumbai, has an MBA from IIMA. After 17 years in
private industry, he shifted to School Education, since
his basic interest and core competency is in
education. His experience ranges from being the
Bursar of Rishi Valley School to a Principal, TeacherTrainer and Educational Consultant. He has recently
retired from the Reliance School, Jamnagar. He is
very much interested in Primary Math and has worked
with teachers in his own school and conducted many
workshops in this area. He wishes to acknowledge
the Late Mr.P.K.Srinivasan who has been his guiding
force and he feels he owes all his Math
understanding to him.
Some Happy Drills for Practising Math skills:
1. Number Play
a. Pick up any 6 digits between 1 and 9.
b. Without repeating the digits, make as many 1 digit, 2 digit and 3 digit numbers.
c. How many numbers do you get in all?
d. Arrange all of them in ascending order.
e. Sort them into Odd & Even numbers and Prime & Composite numbers.
f. In case of the Composite numbers, write down all the factors.
2. 1234
a. Write numbers 1,2,3 & 4 in the same sequence.
b. Insert any accepted mathematical operator like +, -, x, ÷, () etc. You can use others also as long as
they are accepted in Mathematics.
c. The numbers can be above or below others as in 23 . But 3 should come after 2.
d. Insert them in such a way that the result is any number between 0 and 99.
e. E.g 1+2+3+4=10
f. Challenge: In how many ways can you get the result 1?
3. Odd & Even chain
a. Take any 2 digit number
b. If it is even, divide by 2 and write the number below the first number.
c. If it is odd, multiply by 3 then add 1 and write the resulting number below the first number.
d. Repeat process until you get a surprise result.
Look for some more happy drills provided by the speaker in our next issue.
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MDA Newsletter
September 2014
Awareness & School Centres - A Summary
An Exclusive Awareness Wing for Dyslexia
Awareness of dyslexia is one of the prime objectives
of MDA. We have been doing these in both English
and Tamil and in the print and electronic media, since
our inception. However, we do realise this needs to
be an ongoing process and touch various people in
the community so that no child goes unidentified.
With the tremendous potential these children have,
identification and intervention are critical. The earlier
it is done, the better it is for the child. Considering
this, at the beginning of this academic year, an
awareness wing was started in order to go about
awareness with more vim and vigour than before.
Schools, social clubs, and corporate organisations
have been our target. The response has been
excellent with many of the above coming forward with
wanting awareness programmes as well as follow-up
workshops.
Mrs.Harini Mohan has conducted awareness
programmes at JRM School, JRK School, VanaVani,
Viswaksena Global School, Amrita Vidyalayam, Vel’s
Vidyashram, MGR Janaki College, a radio programme
at M.O.P.Vaishnav College, Latent View and TCS.
Setting up of School Resource Rooms with MDA’s Collaboration
Setting up of Resource Rooms in schools has been
one of MDA’s earliest activities in the 90s. While about
ten schools came forward to set up centres at that
time, presently only five of the centres are
functioning. They have been consistently and
successfully helping children for a decade and more,
since their inception.
At Samyukth 2013, the Principals of these five
schools were felicitated with a citation commending
the help provided to the dyslexic children in their
schools. They surely are the role models to the other
schools, having helped many children with dyslexia
cope with their problems. The last two years have
seen a revival of interest by schools to have a
resource room of their own.
Why a School Resource Room?
When children get remedial help within the school
itself it has many advantages. It saves time after
school, with no travelling involved and gives the
scope for the class teacher and remedial teacher to
work in tandem. Children often write the tests and
exams in the resource room where the paper is read
out, the child writes without any distractions and could
be given the extra time needed.
So what does setting up a Resource Room in the
school involve?
It mainly needs strong conviction on the part of the
school authorities to want to help children with
dyslexia. The other needs are:
Space: A large classroom or two small ones
Remedial teachers: At least two trained in handling
children with dyslexia.
Some financials for buying materials and books.
How does MDA help?
The school enters into an arrangement with MDA.
MDA provides help starting from conducting
awareness programmes for teachers and parents,
workshops for teachers to actually setting up the
Resource Room.
This is followed by weekly monitoring which involves
screening, planning, implementation of the lesson
plans, documentation and review.
What are some of the school projects?
• A pilot project was done earlier on, and a Resource
Room was set up for the Junior and the Senior
students of Ramakrishna Matriculation School,
Bazullah Road.
• The next Resource Room is at Vana Vani Matriculation Higher Secondary School, IIT campus. With
two teachers trained at MDA, they have started
their operations helping the Primary class children.
•
Amrita Vidyalayam has joined the elite group
of schools that have their own Resource Room in July
2014. With two MDA trained teachers, many students
have been identified as part of the early intervention
programme in Class 1 itself. A pre-skill training
programme for these students have been started,
while screening for each child is going on
Continued on Page 6
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MDA Newsletter
September 2014
Children’s Page
Mango tree by V. Jhanavi, class 7
I am a mango tree. Everyone likes my fruit because it
is fresh and ripe. I don’t like children throwing stone
on me. I become available in plenty during the
summer month.
Jackfruit is a good source of Potassium, Magnesium
and Iron. The wood is widely used in manufacturing
musical instruments, construction, furniture, doors
and windows. The root of jackfruit tree is a remedy for
skin diseases. All the parts of tree are very useful.
Jackfruit tree by Daval Lakhani, class 7
Apple tree by Siddartha, class 7
Hi, I am 30 year old jackfruit tree. Someone ate
jackfruit and threw the seed out. The seed got
stamped by someone and got buried into the sand.
Then I grew into a sapling in a year. After 8 years, I
grew into a big tree and started bearing fruit.
Everyone tasted my fruit and loved it.
I am an apple tree. I give apple. I am very big. I am
near Ananya School. Children like my apple but
people cut me.
I give oxygen for people. My fruits have lot of
nutrients. There is a proverb “an apple a day keeps
doctor away”. The smell of my apples attracts the
children. Ananya school children take my apple and
eat. My branches are big and I give shade to
everyone. Sometimes my apples fall on ground and
get spoilt. This makes me very sad.
Continued from Page 5
simultaneously. This endeavour is possible only with
the whole-hearted support of the management,
principal and teachers.
In the pipeline are many more schools who want to set
up their Resource Rooms. Business organisations
are coming forward to do this as part of their
Corporate Social Responsibility and want to run an
after-school centre in places where there is no proper
remedial help available.
The sky is the limit! This is the beginning. Many more
such Resource Rooms will be coming up in the near
future. These would provide the necessary support
for children with specific learning difficulties. Our
dream is that each school has its own facility to
ensure that no dyslexic child is left behind.
Contact person: Mrs. Vilasini Diwakar
Dr. Emma Gonzalves is no more. She was a counsellor par excellence and has helped both the young
and old and many of our parents and children. This is indeed a big loss to our community and leaves a
void that is hard to fill.
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MDA Newsletter
September 2014
News at MDA / ANANYA
Winners always
Eight students of Class X cleared their Boards in May with ease. Seven of them have gone back to Mainstream
Schools to do Plus 2 and one has stayed back at Ananya to continue his Senior Secondary through NIOS. All
six of the NIOS Class XII students have gone to various city colleges pursing courses in Arts, Music and
Commerce.
The Annual Soroptimist International competitions held in the month of July saw our students winning prizes in
art, music and dramatics. Darshan of Junior school, Sarayu, Sumedha, Joe Pinto, Rosy, Neha, Mirudula,
Keerthana, Nandhini, Gautam, Christopher, Amarnath, Mahatheeswaran and Anoush from the Senior school
were the winners.
In-house mini-projects
This year the junior school children had two projects; sight word reading and phonemic awareness that are the
most essential components of skill building for reading. The children became teachers and showed how they
have learnt to read better to the visitors. Keep it up children!
Summer workshop
The need of the hour is to conduct bilingual workshops in both English and Tamil. This will enable many more
people to understand how to identify the dyslexic child and how to help. We tried two such endeavours in the
month of May which were of longer duration. Our 5-day training at Madurai was organised by Manickavasagam
Trust for about fifty teachers from schools under the Thiagarajar Group. It was a first in conducting a fullfledged training programme for mainstream teachers outside Chennai and in bilingual mode too. Then, a 3-day
workshop was also conducted in Chennai in the month of May. Parents, teachers, educators as well as those
interested in knowing more about dyslexia benefited from it. The bilingual workshop and training was well
received and could be a forerunner for many more to come.
The 15th Annual Sports Day
The Sports Day was celebrated with the usual vigour and enthusiasm at the RKM
playground off G.N. Chetty Road on 12th September. Ms. Sharanya Vidyut, the
Junior National Tennis Champion was the chief guest who gave away the prizes to
the children. There was another special guest on that day, Mrs.Nirmala
Venkateswaran, who has been our Consultant Occupational Therapist for nearly
two decades. She addressed the parents and teachers giving some valuable
inputs about these children. We are tremendously thankful to Mrs.Nirmala for all
the help given to us directly and through intervention to many of our children. The
Chennai OT fraternity, learning centres as well as the parents are going to feel the
void and miss the expertise and experience of Mrs. Nirmala, who is settling down in
Cochin. We wish her all the best and hope to have some more opportunities to
interact with her in the years to come.
Announcement
Weekend Teacher Training
♦ MDA announces its Weekend Training Programme for eight Saturdays starting
from 25th October.
♦ Open to Mainstream Teachers, Counselors and Therapists who are working
with children with learning issues.
♦ Interested persons can call MDA office for more details.
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MDA Newsletter
September 2014
12.05.14 & 23.05.14
Workshop for the second year Special B.Ed trainees and a half-day training
programme for first year Spl.B.Ed trainees at SPASTN, conducted by Geetha.R.
30.05.14
Workshop for Junior and Senior School teachers at Kalaimagal Vidyalaya, Royapuram
conducted by Sujatha.R, Latha.V and Harini.M.
03.06.14
Dyslexia Workshop at A.M.Jain School Meenambakkam conducted by Subha.V and
Harini.M.
19.06.14
Dyslexia Workshop at Airforce School Avadi conducted by Subha.V and Harini.M.
21.06.14
Workshop for the Resource Room Teachers of BVM Group of Schools at Bala Vidya
Mandir, Gandhi Nagar conducted by Subha.V and Savithri.K.
05.07.14
Workshop for the Junior teachers at Chennai Public School conducted by Sujatha.R
and Latha.V.
05.07.14
Workshop at Vanavani School in IIT campus conducted by Subha.V and Latha.V.
11.07.14
Math Workshop for mainstream teachers from Muscat, Oman as part of the Inclusion
Training offered by Vidyasagar conducted by Sujatha.R.
12.07.14
Inter-school meet on Inclusive Education organized by Mirra Foundation, Chennai.
Janaki.R participated.
21.07.14
Start of 8-week Intensive Teachers Training Course at MDA.
25 & 26 07.14
MDA stall at ‘Seva Mela’ organized by CIOSA at Ethiraj College for Women.
29.07.14
Dyslexia Workshop at Amrita Vidyalayam School conducted by Sujatha.R and Latha.V.
29.07.14
Workshop on remedial strategies for forty volunteers who are helping children in
Pondicherry, organized by Dr.B.Balachandar, conducted by Sujatha.R and Latha.V.
18.08.14
1-day workshop organized by Alpha to Omega on Developmental, Emotional and
Behavioural disorders attended by Vilasini.D and Viasalskhi.I.
Our Editorial Team - Indu Ramesh, Kamala Ramaraj, Geetha Raghavan and Vilasini Diwakar
For Private Circulation Only
BOOK POST
If undelivered, please return to:
Madras Dyslexia Association
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T. Nagar, Chennai 600 017
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